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| FIELD | Mathematics |
|---|---|
| DATE | April 19 (Thu), 2018 |
| TIME | 14:00-15:30 |
| PLACE | 1423 |
| SPEAKER | Kwok Kin Wong |
| HOST | Hwang, Jun-Muk |
| INSTITUTE | KIAS |
| TITLE | Zariski closures of images of algebraic subsets under uniformization map of complex unit balls |
| ABSTRACT | Let $S$ be an irreducible algebraic subset of the complex unit ball $\mathbb{B}^n$ and $\pi: \mathbb{B}^n\rightarrow X_\Gamma= \mathbb{B}^n/\Gamma$ is the universal covering map to a quotient by irreducible torsion free lattice. We show by complex differential geometric techniques that the Zariski closure $Z=\overline{\pi(S)}^{Zar}$ in $X_\Gamma$ is a totally geodesic subset. It is an analogue of the hyperbolic Ax-Lindemann-Weierstrass conjecture in rank $1$ case, especially where the arithmeticity is unnecessary. The result is the main theorem of a recent preprint of Mok: http://hkumath.hku.hk/~imr/IMRPreprintSeries/2017/IMR2017-2.pdf. |
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